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Trigonometric Ratios Of Compounds — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compounds1 Mark
Question
If $\frac{\pi}{2}<​\text{x}<\frac{3\pi}{2},$ then write the value of $\sqrt{\frac{1+\cos2​\text{x}}{2}}$
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Answer

Since $\frac{\pi}{2}<\theta<\frac{3\pi}{2}\Rightarrow2^{\text{nd}}\ \&\ 3^{\text{rd}}$ quadarant Now, $\sqrt{\frac{1+\cos2\theta}{2}}=\sqrt{\frac{2\cos^2\theta}{2}}$ $-\cos\theta$ (-ve sigh due to $2^{nd}$ $3^{rd}$ quad) $=-\cos\theta$

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